MathAudit

Paper metadata

Original submission
January 31, 2021
Claimed MSC
11J20
arXiv categories
math.NT
Comments
9 pages

Abstract

We improve on a result by Svetlana Jitomirskaya and Wencai Liu dealing with inhomogeneous Diophantine approximation in the coprime setting.

AI-generated audit

Audit summary

Audited against arXiv v1

Not a correctness certificate. A “Correct” result may include yellow typos or minor formal corrections that do not affect substantive soundness. It means this audit found no unresolved substantive error under the stated criteria; it does not replace expert scrutiny or formal verification.

Current report

Detailed mathematical audit

Generated August 20, 2026
01Statements2 reported findingsCorrect

The construction of uncountably many irrational shifts with the stated lower bound for all primitive lattice points is correct.

Theorem 1Correct

The nested continued-fraction and congruence construction excludes primitive points

Pages 2 and 6–9 · Theorem 1 and final construction · arXiv:2102.00543v1

The Chinese-remainder arrays force every lattice point in the relevant moving rectangle to have a common prime divisor. The rapidly growing continued-fraction digits make those rectangles cover all sufficiently large candidate approximants, while the nested choices leave uncountably many limit pairs.

Full paper, version 1 ↗
Local vector notationTypos · no status impact

Several indices, endpoints, and planar coordinates are local typos

Pages 6–9 · Remark 2, Section 4, and proof of Theorem 1 · arXiv:2102.00543v1

In Remark 2, ∏j=1kak\prod_{j=1}^k a_k must be ∏j=1kaj\prod_{j=1}^k a_j. The convergence estimate in Section 4 has one spurious +1+1 on the index of PP. In case 101^0, the three occurrences of Pkλk+1P_k\lambda_{k+1} must use Pℓλk+1P_\ell\lambda_{k+1}, where ℓ=⌊k/2⌋\ell=\lfloor k/2\rfloor. The second endpoint is (bk+1−ℓvk,ck+1−ℓuk)(b_{k+1}-\ell v_k,c_{k+1}-\ell u_k), and the later vector printed with coordinates (ck+yuk,bk+yvk)(c_k+yu_k,b_k+yv_k) must be (bk+yvk,ck+yuk)(b_k+yv_k,c_k+yu_k). The adjacent recurrence and displayed first-coordinate bounds uniquely fix all of these repairs.

02Proofs2 reported findingsCorrect

The prime-grid, continued-fraction, and nesting arguments are complete after the local point-label corrections.

Sections 2–3Correct and complete

The Chinese-remainder arrays propagate through the convergents

Pages 2–6 · prime arrays, affine lattices, and the recursion for Zk\mathfrak Z_k · arXiv:2102.00543v1

The prime blocks assign a common prime divisor to every small coefficient pair, and the Chinese remainder theorem produces compatible residue classes Xk,YkX_k,Y_k. The divisibility imposed on each next partial quotient makes the recurrence for Zk+1\mathfrak Z_{k+1} move from Lk\mathfrak L_k into Lk+1\mathfrak L_{k+1}. Coprimality of the successive moduli leaves an admissible positive choice of λk+1\lambda_{k+1} near the required midpoint.

Sections 2–5Correct and complete after the stated repairs

The covering scale matches the prime-grid obstruction

Pages 2–9 · prime construction and proof of Theorem 1 · arXiv:2102.00543v1

The prime product has the required logarithmic asymptotic, the next partial quotient dominates that product, and each primitive candidate is forced into a congruence cell carrying a common divisor. The independent free choices at infinitely many stages yield uncountably many limits.

03Novelty0 reported findingsNo non-novelty findings

No non-novelty findings.

Detailed audit reportFull reasoning, manuscript locations, and references.
Open report PDF ↗

Author response

Challenge an audit finding

Local workflow preview

A listed author may submit formal evidence that an audit is inaccurate. The response would be considered in a fresh AI re-evaluation; it would not edit the audit automatically.

Paper
arXiv:2102.00543v1
Authors listed
Nikolay Moshchevitin
Audit date
August 20, 2026
  1. 01Establish identityMatch an authenticated scholarly identity to this paper.
  2. 02Submit evidenceIdentify the finding and give a formal mathematical response.
  3. 03Re-evaluateA separate agent checks the response and records a disposition.
Recommended production method

Authenticate with ORCID, then require an exact arXiv match

MathAudit should accept the identity only when ORCID OAuth authenticates the claimant's iD and this exact arXiv paper appears in arXiv's public authority feed for that iD. A matching name alone is not sufficient.

ORCID OAuth and arXiv authority-record lookup are not connected in this local prototype.

Email fallback for papers without a linked ORCID

A production fallback could send a one-time link only when the submitted address matches an independently maintained author-contact allowlist for this paper. MathAudit must return the same message for every address so the form cannot reveal which contacts are on that list.

This demonstration does not send, store, or compare the address.

Structured response preview

This form remains unavailable until production identity verification succeeds. Nothing entered here is submitted.

This panel never establishes authorship in the local prototype. A production result should be described narrowly as an authenticated ORCID match or control of a separately allowlisted author-contact mailbox.